How does a government facilitate comprehensive care for its constituents without sacrificing equity?

How does a government facilitate comprehensive care for its constituents without sacrificing equity?

First, what is equity? equity is the residual claim or interest of the most junior class of investors in assets, after all liabilities are paid. If valuations placed on assets do not exceed liabilities, negative equity exists. In an accounting context, Shareholders' equity (or stockholders' equity, shareholders' funds, shareholders' capital or similar terms) represents the remaining interest in assets of a company, spread among individual shareholders of common or preferred stock.  

The government facilitate comprehensive care for its constituents through many different programs such as unemployment, medicare, and social security.  This is possible because everyone that works pays or supports all these programs for everybody that pulls from it.  This is a good idea but I do not know if it is practical because these systems are currently draining our government and is a creating a huge problem for us.